Infinitely many sign-changing solutions for an asymptotically linear and nonlocal schrodinger equation

In this article, we consider the  nonlocal schrodinger equation $$ -\mathcal{L}_K u+V(x)u=f(x,u),\quad x\in\mathbb{R}^N,  $$ where \(-\mathcal{L}_K\) is an integro-differential operator and  \(V\) is coercive at infinity, and \(f(x,u)\) is asymptotically linear  for \(u\) at infinity. Combining mini...

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Veröffentlicht in:Electronic journal of differential equations 2025-01, Vol.2025 (1-??), p.7
Hauptverfasser: Qiu, Ruowen, You, Renqing, Zhao, Fukun
Format: Artikel
Sprache:eng
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Zusammenfassung:In this article, we consider the  nonlocal schrodinger equation $$ -\mathcal{L}_K u+V(x)u=f(x,u),\quad x\in\mathbb{R}^N,  $$ where \(-\mathcal{L}_K\) is an integro-differential operator and  \(V\) is coercive at infinity, and \(f(x,u)\) is asymptotically linear  for \(u\) at infinity. Combining minimax method and invariant set of  descending flow, we prove that the problem possesses infinitely many  sign-changing solutions.  For more information see https://ejde.math.txstate.edu/Volumes/2025/07/abstr.html
ISSN:1072-6691
1072-6691
DOI:10.58997/ejde.2025.07